An operational amplifier (or "op amp") having an inverting (or negative) input terminal, a non-inverting (or positive) input teminal, and an output terminal is typically employed in an amplifier system with a feedback network connected between the output and input terminals. The op amp amplifies an input signal received at the input terminals (or simply "inputs") to produce an output signal at the output terminal (or simply "output"). The gain in the negative feedback loop is .mu..beta. where .mu. is the forward gain of the op amp and .beta. is the gain of the negative feedback network. Depending on the configuration, .mu. and .beta. may be either voltage gain or current gain.
When the input signal varies at some frequency, the output signal varies similarly. At low frequency, they are substantially in phase. As frequency increases, the phase of the output signal lags progressively behind the phase of the input signal. The loop gain .mu..beta. falls off. The system can become unstable. If the phase difference between the signals reaches 180.degree. while .beta. is greater than 1, the system oscillates because the feedback is positive.
The minimum acceptable stability margin is considered to occur when the loop phase difference equals 135.degree. at the point where .mu..beta. is 1. This roughly translates into the stability rule that the loop gain not fall off more than 9 dB/octave out to the unity-gain frequency.
A feedback network for a system utilizing an op amp is often provided after op amp design is completed. The precise amplitude characteristics of the network thus cannot be taken into account in designing the op amp. The design is typically based on the "worst-case" assumption that the negative feedback gain is one. The resulting stability criterion is that the forward gain .mu. of the op amp not roll off more than 9 dB/oct. out to the frequency where .mu. is 1.
Perhaps the easiest way to meet this stability criterion is with a single transconductance amplifier stage. FIG. 1 generally shows a conventional differential stage A of this type. FIG. 2 illustrates typical internal details for stage A which centers on emitter-coupled NPN transistors QX and QY. Their bases are connected to its inputs to receive voltages V.sub.I- and V.sub.I+ whose difference is the amplifier input signal V.sub.I. Although stage A is basically a transconductance amplifier--i.e., a voltage-to-current converter, the load impedance converts stage A into a voltage amplifier. Its output signal is a voltage V.sub.O supplied at the QX collector.
The frequency response of stage A is largely determined by its single dominant pole dependent on the parasitic capacitance CPO at the output. Referring to FIG. 3, it shows asymptotes for how .mu. varies with frequency f for stage A. The gain drops 6 dB/oct. as the frequency f.sub.O of the dominant pole is passed and then 6 dB/oct. more as the higher pole frequency f.sub.L that limits the bandwidth is passed. Bandwidth-limiting frequency f.sub.L, which is a characteristic of the overall amplifier system and cannot be altered easily, occurs beyond the unity-gain frequency f.sub.U. Stage A thus automatically satisfies the foregoing stability criterion since the gain roll-off is less than 9dB/oct. between f.sub.O and f.sub.U. No frequency compensation is needed. However, the maximum gain is typically on the order of 40 dB. This is much too low for many applications.
The gain can be increased by arranging two transconductance amplifier stages in cascade. FIG. 4 generally shows how this is done in a conventional 741 op amp as, for example, described by Gray et al in Analysis and Design of Analog Integrated Circuits (John Wiley and Sons), 1977, pages 420-426 and 515-521. In the 741, voltage V.sub.I is differentially supplied to the inputs of a differential stage A' whose output is connected to the inverting input of an inverting stage A". Its output provides voltage V.sub.O. A compensating capacitor C is connected between the A" input and output. This connection enables the combination A" and C to act as a current-to-voltage converter. The overall amplifier thereby provides voltage amplification.
Two dominant poles largely determine the frequency response of this two-stage amplifier, one dependent on the parasitic capacitance CPO at the amplifier output and the other dependent on the parasitic capacitance CPA at the A" input. FIG. 5 depicts the asymptotic gain variation for FIG. 4. The upper curve in FIG. 5 represents how the frequency response would appear if capacitor C were absent, while the lower curve represents the actual compensated response. The pole frequencies associated with capacitances CPO and CPA are respectively referred to as f.sub.O and f.sub.A. In passing each of frequencies f.sub.O, f.sub.A, and f.sub.L, the gain roll-off increases 6 dB/oct.
In the absence of capacitor C, f.sub.O and f.sub.A would be at respective starting points f.sub.OS and f.sub.AS where .mu. is greater than 1. The combination A' and A" would not meet the foregoing stability criterion since .mu. drops 12 dB/oct. after f.sub.AS is passed.
Capacitor C provides frequency compensation by splitting the dominant poles further apart. Lower pole f.sub.O moves down to final position f.sub.OF, while higher pole f.sub.A moves up to final position f.sub.AF beyond unity-gain frequency f.sub.U. The gain rolls off no more than 6 dB/oct. out to f.sub.U to meet the stability criterion. The maximum gain is typically on the order of 80 dB. Although an improvement, this is still too low for many applications.
In U.S. Pat. No. 4,243, 943, E. Cherry approaches the gain/stability problem with an amplifier typically having three or more stages arranged in a nest of differentiating feedback loops for frequency compensation. The loops are normally centered on the output stage of the amplifier. The basic objective in Cherry is to maximize the return difference around the output stage. The compensation scheme in Cherry involves pole-zero cancellation in which frequency zeros are employed to shift frequency poles to acceptable locations. This is a complex process which severely limits the use of Cherry.